Question 7 in the Baptist Catechism begins with “God is Spirit,” and moves secondly to infinity. Popularly, infinity is a confusing term. What does it mean? It seems like many think of infinity in terms of the large-ness of any one particular thing. We are used to hearing expressions like, “space goes on for infinity,” or “the road appears to stretch for infinity.” We often use infinity to communicate a quantity that cannot be comprehended. But this is not a precise use of the term.
Infinity is not a number and so it does not quantify anything. So, infinity, properly speaking, cannot apply to the quantification of things which make up an incomprehensible whole. So, what is infinity?
Richard A. Muller writes:
The divine infinitas can also be described negatively and positively. It is not an infinity of corporeal quantity or extension but rather an infinity defined by the absence of limit; positively, it is an infinite superiority over all things.
Negatively, infinity speaks to the absence of limitation. It says something about what X is not. If X is infinite, then limitation is absent to X. Positively, infinity applies to that which is beyond all created things, a transcendence above the created order.
God & Infinity
When we say “God is infinite,” what do we mean? Infinity is best thought of in terms of what God is not. God is not bound my limitation. If we could think of limitation as the existence of potency in any given object, this will help us frame infinity within the context of the doctrine of simplicity previously discussed.
If God is pure actuality, then He is devoid of potency. That is to say that God is not potentially something other than what He is. If God was potential, then there would need to be other factors outside Himself that could actualize that potential. If this were the case, God would be dependent upon those external factors to be who He is. Moreover, God would not be perfect since the existence of potency is, by definition of the term, imperfection. Pure act is perfection in contrast to potency, which is imperfection.
Because God is pure act, He is perfect and being perfect He is infinite since perfection must be devoid of limitation. Now, absence of limitation must be thought of externally. By nature, there are things God cannot do. God cannot sin; God cannot change; God cannot become not God; God cannot make something or someone higher than Himself because He would then be not God. These are all things God cannot do in virtue of who God is. God cannot make a higher being than Himself because God Himself is that which nothing greater can be conceived. God cannot sin because God is light and in Him there is no darkness.
These limitations are not limitations on God’s nature coming upon Him from outside Himself. Rather, who God is is the definition of perfection. God cannot sin because He is perfect. If God could sin, He would not be perfect. God cannot become not God because He is perfect. Infinity does not entail the capacity to do anything or become anything whatsoever. Infinity is what God is not, that is, God is not limited by blights like sin or real potency. These things are imperfections and would therefore make God a finite creature.
What God cannot do is indicative of His infinite perfection rather than a subtraction from it.
 Richard A. Muller, Dictionary of Latin and Greek Theological Terms, 172.